Question

a patient is not allowed to have more than 300 milligrams of cholesterol per day from a diet of eggs and meat. each egg provides 150 milligrams of cholesterol. each ounce of meat provides 100 milligrams of cholesterol. completes parts (a) through (c) below.
the inequality is 150x + 100y ≤ 300. (use integers or decimals for any numbers in the expression.)
b. graph the inequality. because x and y must be positive, limit the graph to quadrant i only. choose the correct graph below.
a.
b.
c.
d.

Explanation:

Step1: Rewrite the inequality in slope - intercept form

Starting with $150x + 100y\leq300$, solve for $y$. First, subtract $150x$ from both sides: $100y\leq - 150x + 300$. Then divide by 100: $y\leq-\frac{3}{2}x + 3$.

Step2: Find the x - intercept

Set $y = 0$ in the equation $y=-\frac{3}{2}x + 3$. Then $0=-\frac{3}{2}x+3$. Add $\frac{3}{2}x$ to both sides: $\frac{3}{2}x=3$. Multiply both sides by $\frac{2}{3}$ to get $x = 2$.

Step3: Find the y - intercept

Set $x = 0$ in the equation $y=-\frac{3}{2}x + 3$. Then $y=3$.

Step4: Analyze the inequality for graphing

Since $y\leq-\frac{3}{2}x + 3$ and $x\geq0,y\geq0$ (restricted to quadrant I), the region is below the line $y =-\frac{3}{2}x+3$ and in the first - quadrant. The line $y =-\frac{3}{2}x + 3$ is solid (because of $\leq$) and passes through the points $(0,3)$ and $(2,0)$.

Answer:

A.